Find an example of an arithmetic sequence that has an explicit pattern. Then determine the formula for that sequence and use it to define the given term.

11)

5, -5, -15, -25,  ...

-5-5 = -10;   -15-(-5) = -10;   -25-(-15) = -10   ⇒  this is an example of arithmetic sequence that has explicit patern (evey next term is 10 less than previous one)

difference:  d = -10

first term:  a = 5

so the formula:

and:

12)

19, 26, 33, 40,  ...

26-19 = 7;   33-26 = 7;   40-33 = 7   ⇒  this is an example of arithmetic sequence that has explicit patern (evey next term is 7 more than previous one)

difference:  d = 7

first term:  a = 19

so the formula:

and:

13)

-20, -29, -38, -47,  ...

-29-(-20) = -9;   -38-(-28) = -9;   -47-(-38) = -9   ⇒  this is an example of arithmetic sequence that has explicit patern (evey next term is 9 less than previous one)

difference:  d = -9

first term:  a = -20

so the formula:

and:

11)

1, -2, 3, -4,  ...

-5-1 = -3;   3-(-2) = 5 ≠ -3   ⇒  this is NOT an example of arithmetic sequence

however it has explicit patern:

so:

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0